Inventory
Chapter 6
Inventory System
Inventory: is the set of the items that an organization holds
for later use by the organization.
An Inventory System is a set of policies that monitors and
controls inventory. It determines how much of each item
should be kept, when low items should be replenished, and
how many items should be ordered or made when
replenishment is needed.
The Functions of Inventory
• Provide a stock of goods to meet anticipated
customer demand and provide a “selection” of goods
• Decouple suppliers from production and production
from distribution
• Allow one to take advantage of quantity discounts
• To provide a hedge against inflation
• To protect against shortages due to delivery
variation
• To permit operations to continue smoothly with the
use of “work-in-process”
Disadvantages of Inventory
• Higher costs
– Item cost (if purchased)
– Ordering (or setup) cost
• Costs of forms, clerks’ wages etc.
– Holding (or carrying) cost
• Building lease, insurance, taxes etc.
• Difficult to control
– Uncertain demand
– Uncertain lead time
Types of Inventory
•
•
•
•
•
•
Raw materials
Purchased parts and supplies
Work-in-process
Component parts
Tools, machinery, and equipment
Finished goods
Raw material
Component parts
and supplies
Finished
goods
Work-in process In-process
(partially completed) products
Purchasing part
Tools, machinery, and equipment
Types of Inventory
Two forms of Demands
Independent Demand: are those items that we sell to customers.
Ex. Ford Motor Company, their main independent demand will be the
cars, trucks and van that they sell.
A small part of the independent demand would the parts that they sell
to customers.
Finished products
Based on market demand
Requires forecasting
Dependent Demand: are those items whose demand is determined
by other items. When Ford Motors Company has demand for a car,
that translates into demand for four tires, one engine, one
transmission, and so on. The items used in the production of that car.
Parts that go into the finished products
Dependent demand is a known function of independent demand
No forecasting is required
Reasons To Hold Inventory
• Meet unexpected,seasonal, cyclical, and
variations demand
• Take advantage of price discounts
• Hedge against price increases
• Quantity discounts (To get a lower price)
• To decouple work-centers
• To allow flexible production schedule
• As a safeguard against variations in delivery time
(lead time)
Costs of Inventory
Visible Costs of Inventory.
They are holding, shortage, reordering, and
setup cost.
Hidden Costs of Inventory
Costs result from longer or uncertain leadtime, or by following bad inventory control
system
The Visible Cost of Inventory
1.
2.
Holding Cost: These are all the cost the organization
incurs in the purchase and storing of the inventory. They
include the cost of financing the purchase , storage costs,
handling costs, taxes, obsolescence, pilferage, breakage,
spoilage, reduced flexibility, and opportunity costs. They
are also called Carriage cost. High holding cost favor low
inventory levels and frequent replacements and vice
versa.
Setup Cost: This is the cost of switching a production line
from making one product to making a different product.
Setup cost apply only to items the organization produces
itself. High setup cost favors large production runs and
the resulting larger inventory and vice versa.
The Visible Cost of Inventory
3. Ordering Cost: This is the cost of placing an order for an
item the organization purchases. It include placing the
order, tracking the order, shipping costs, receiving and
inspecting the order and handling the paperwork. High
ordering costs favor fewer orders of larger size and
resulting large inventory and vice versa.
4. Shortage Costs: This is the cost to the organization of
not having an item when it is needed. These costs
include loss of goodwill, loss of sale, loss of a customer,
loss of profits and late penalties. Many of these costs
are difficult or impossible to measure with any accuracy.
High shortage cost favor large inventory and vice versa
Cyclic Inventory Control
Inventory control at Ware-Mart-Example
The purchasing department is offering 7 alternative cycles
and times (T):
1.
Order every week, 52 times per year, T=1 week
2.
Order every second week, 26 times per year, T=2
weeks
3.
Order every month, 12 times per year, T=1 month
4.
Order every second month, 6 times per year, T=2,
months
5.
Order quarterly, 4 times per year, T= 3 months
6.
Order semiannually, twice per year, T=6 months
7.
Order every year, once a year, T=1 year
Brent estimates :
Yearly demand rate =
12000 pots
Quarterly demand
= 3000 pots
Average inventory
= 1500 pots
Every day demand
= 100 pots
Price/ pots
=
$6.75
Corporate holding cost =
holding cost
20% of the purchasing cost for
Unit Annual holding cost = 0.20 *6.75=$1.35
Forecast for the annual holding cost = 1500 * 1.35 = 2025
Ordering cost is between $25 and $30
Average Ordering cost
=
$28
Annual Ordering cost
=
4*28
= $112
Annual Combined Cost
= Annual Ordering Cost + Annual
Holding cost
=
$2025+$112 = $2137
Ware-Mart
Order Plans For Pots
Model
Annual demand
D
Cost per unit
C
Interest rate to hold
i
Ordering cost
O
Quantity each order
D/N
Number of orders
N
Unit holding cost
H=C*i
Annual holding cost
QH/2
Annual ordering cost
NO
Combined cost
QH/2+NO
Annual purchase cost
DC
Total cost
Weekly Bi-Weekly
Orders
Orders
12,000
12,000
$6.75
$6.75
20%
20%
$28.00
$28.00
230
461
52
26
$1.35
$1.35
$155
$311
$1,456
$728
$1,611
$1,039
$81,000
$81,000
$82,611
$82,039
$90,000
$88,000
$86,000
$84,000
$82,000
$80,000
$78,000
52
26
12
6
4
Orders Per Year
2
1
Monthly Bi-Monthly Quarterly Semi-Annual
Orders
Orders
Orders
Orders
12,000
12,000
12,000
12,000
$6.75
$6.75
$6.75
$6.75
20%
20%
20%
20%
$28.00
$28.00
$28.00
$28.00
1,000
2,000
3,000
6,000
12
6
4
2
$1.35
$1.35
$1.35
$1.35
$675
$1,350
$2,025
$4,050
$336
$168
$112
$56
$1,011
$1,518
$2,137
$4,106
$81,000
$81,000
$81,000
$81,000
$82,011
$82,518
$83,137
$85,106
Smallest
Annual
Orders
12,000
$6.75
20%
$28.00
12,000
1
$1.35
$8,100
$28
$8,128
$81,000
$89,128
• Purpose of the inventory system is to
decide how much to order and when
• Objectives of inventory system
• Keep enough inventory to meet customer
demand
• Control inventory costs
According to that there are different models
for the inventory
Inventory Control Models
Parameters
Ordering cost
Holding costs
Stock out costs
Demand (Certainty,Uncertainties)
Variables
Time sequence of
ordering
Quantity sequence of
ordering
Model
Performance
measure
Profit
Cost
Service level
Influence Chart for selecting Inventory Controls Models
Inventory Control Models
Probabilistic
Deterministic
Periodic review model
Also known as a Fixed order
period models
– Single-period models
– Multi-period models
Continues review model
Also known as a Fixed order
quantity models
– Economic order quantity EOQ
– Production order quantity
– Quantity discount
Triggered policy
Quantity triggered model
Time triggered model
Inventory Controls Models
Probabilistic Model: Where performance measures use expected
values in realistic cases which involves uncertainty.
Deterministic Models: are sufficient by ignoring uncertainty , provided
the decision maker takes both qualitative and quantitative factors
into account.
Continuous Review Models: Assumes that inventory levels are
monitored continuously and that orders are placed depending on the
level of inventory.
Periodic Review Models: assume that the monitoring is performed only
at a stated times, such as monthly or quarterly.
Fixed Order Quantity Models: assume that a constant quantity is order
each time an order is placed.
Fixed Order Period Models: assume that a ordering cycle is
fixed, such as 1 week or 1 month
Multi period Models: assumes that the orders will be placed
repeatedly.
Single Period Models: deals with situations in which only single
orders is placed.
Quantity-Triggered Models: specify ordering when the inventory
level sinks to a stated quantity.
Time-Triggered Models: specify ordering at specific time periods,
such as weekly, monthly or quarterly.
• Continuous inventory systems
– also known as fixed-order-quantity system
– whenever inventory decreases to predetermined
level known as a reorder point, new order is placed
– order is for fixed amount (EOQ) that minimizes total
inventory costs
• Periodic inventory systems
– also known as fixed-time-period system
– inventory on hand is counted at specific time
intervals
– after inventory level determined, order is placed
which will bring inventory back to desired level
– new order quantity determined each time
Deterministic Model
Fixed Order Quantity Models
Economic order quantity EOQ
The Economic Order Quantity
Model (EOQ)
• EOQ model is a deterministic model with a fixed
ordering cycle and fixed quantity ordered.
• The model determines the EOQ that minimizes the
combined total cost of ordering and holding inventory
over a fixed time interval, often one year.
• Excels what-if capabilities make the EOQ a potentially
useful tool by allowing the decision maker to learn about
inventory cost structure while performing the analysis.
• The what-if scenario result can be useful inputs to
decision making.
Economic Order Quantity
(EOQ) Models
• EOQ – the optimal order quantity that
will minimize total inventory carry costs
• Basic EOQ model
– determines optimal order size that
minimizes the sum of carrying costs and
ordering costs
EOQ Assumptions
•Known and constant demand
•Known and constant lead time
•Instantaneous receipt of material
•No quantity discounts
•Only order (setup) cost and holding cost
•No stock outs
Developing the EOQ Model
Parameter
Annual Demand
Unit Holding Cost
Unit Ordering Cost
Performance measure
EOQ Formula
Quantity sequence of ordering
Decision Variable
Optimum order quantity Q*
Minimum annual combined
(holding and ordering) cost
EOQ Model notations
D
Annual Demand
C
Cost per unit
I
interest to hold the Inventory.
H
Expressed as a percentage of costs (C*I)
O
Ordering costs
Q
The Quantity to be ordered
T
Length of the Time
N
Number of annual order
Unit holding Cost (H)= c * i
EOQ or Qopt or Q*=squareroot((2*D*O)/H)
Q* =
2* D*O
H
No. of orders (N)=D/EOQ
Annual Holding Cost (AHC)=H * EOQ/2
Annual ordering Cost (AOC)= O *N
Combine Cost (CC)= AHC+ AOC
Purchase Cost (PC)= D*C
Total Cost= CC + PC
Duration between Orders or Time between orders (T)
= No of Working Days/N
EOQ Models
– Optimal order quantity (Qopt) = square root
[(2OD) / H ]
• Occurs where total cost is at a minimum
• This happens where Holding cost curve
intersects with Ordering cost curve
• Is an approximate value
• Round to nearest whole number
• EOQ model is robust (resilient to errors)
EOQ Model
How Much to Order?
Annual Cost
Order (Setup) Cost Curve
Optimal
Order Quantity (Qopt)
Order Quantity (Qopt)
Purchasing cost C
Holding cost (I)
Ordering cost O
Demand D
Order Quentity
100
400
700
1000
1300
1600
1900
2200
2500
2800
3100
EOQ
$6.75 H
20%
$28.00
12000
1.35
Number of
order per
year
Holding Cost Order Cost
combined cost
120
67.5
$3,360.00
$3,427.50
30
270
$840.00
$1,110.00
17
472.5
$480.00
$952.50
12
675
$336.00
$1,011.00
9
877.5
$258.46
$1,135.96
8
1080
$210.00
$1,290.00
6
1282.5
$176.84
$1,459.34
5
1485
$152.73
$1,637.73
5
1687.5
$134.40
$1,821.90
4
1890
$120.00
$2,010.00
4
2092.5
$108.39
$2,200.89
4000
3500
3000
2500
2000
1500
1000
500
0
100
400
700 1000 1300 1600 1900 2200 2500 2800 3100
[(H)(Q)] / 2
[(O)(D)] / Q
[(O)(D)] / Q + [(H)(Q)] / 2
The graphical figure shows the combined cost as a function of
the order quantity Q.
The annual holding costs are a linear, straight-line function of Q.
The ordering costs are represented by an inverse, diminishing
curve.
The combined cost is U-shaped, starting high, decreasing to
minimum and then increasing again.
The minimum cost is at the bottom of the U, (intersection of the
Holding and Ordering cost) where the slope is zero.
Optimal EOQ
$6.75 H
20%
$28.00
12000
Purchasing cost C
Holding cost (I)
Ordering cost O
Demand D
Optimal Q
Holding cost
Ordering cost
Combined cost
1.35
705.53368
476.23524
476.23524
952.47047
Number of order per year
Time between orders
17.0084
0.058794
0.71
4000
3500
3000
2500
2000
1500
1000
500
0
100
400
700 1000 1300 1600 1900 2200 2500 2800 3100
21.17
Base Case: Order
26 Times a Year
Pots
Demand
12,000
Cost per unit
$6.75
Interest rate to hold
20%
Ordering cost
28
Quantity each order
462
Number of orders
26
Unit holding cost
$1.35
Annual holding cost
$312
Annual ordering cost
$728
Combined cost
$1,040
Annual purchase cost $81,000
Total cost
$82,040
Base Case: Use
EOQ Formula
Demand
Cost per unit
Interest rate to hold
Ordering cost
Unit holding cost
Quantity each order
Number of orders
Annual holding cost
Annual ordering cost
Combined cost
Annual purchase cost
Total cost
Pots
12,000
$6.75
20%
28
1.35
706
$17
$476
$476
$952
$81,000
$81,952
6.7
Economic Production Lot
(EPL) Size
Fundamental Assumptions of
Traditional Manufacturing
• It is expensive to process orders for purchased items,
and quantity discounts are available
– as a result, orders for parts are placed infrequently, in
large quantities
• Setups are lengthy and expensive
– as a result, large batches of each product are made
Production Lot Size
According to traditional thinking,
• Setup costs decrease as production lot or batch size
increases
• Inventory levels and holding cost increases as batch
size increases
• The lot size that minimizes the net cost is called the
Economic Production Lot (EPL)
Kinds of Lots
•
•
•
•
Production or process lot
Purchase or order quantity
Transfer batch
Delivery quantity
Economic Production Lot Size
• The Economic Production Lot (EPL) size model is a
variation of the basic EOQ model.
• A replenishment order is not received in one lump sum
as it is in the basic EOQ model.
• Inventory is replenished gradually as the order is
produced (which requires the production rate to be
greater than the demand rate).
• This model's variable costs are annual holding cost and
annual set-up cost (equivalent to ordering cost).
• For the optimal lot size, annual holding and set-up costs
are equal.
Economic Production Lot Size
Assumptions
– Demand occurs at a constant rate of D items per
year.
– Production rate is P items per year (and P > D ).
– Set-up cost O per run.
– Holding cost H per item in inventory per year.
– Purchase cost per unit C is constant (no quantity
discount).
– Set-up time (lead time) is constant.
– Planned shortages are not permitted.
Production, Demand and
Inventory
60
Economic
Production
Lot
Quantity
50
40
Production
Demand
Inventory
Fluctuating
Inventory
30
20
10
0
1
2
3
4
5
6
Time period
7
8
9
10
EPL or EPQ
Inv
Slope=P-D
Unless you stop production,
since you cannot sell the parts
at the same or faster rate
that you are making them,
your inventory will grow.
Note: P and D should be in
same units
Time
EPL
Slope=P-D
Inv
Slope=-D
H
Start
Prod.
T1
Stop
Prod.
T2
Time
Start
Prod.
Economic Production lot Size
Model
O
Ordering Cost
P
Production rate
t
time need to produce the lot
Q=Pxt
t = Q/P
Maximum inventory = ( P x t) – ( D x t ) = ( P – D ) x t
= ( P – D) x Q/P =(1 – D/P) x Q
Average inventory = (1 – D/P) x Q/2
F = 1 – D/P
is critical in lot size calculations.
To Establish the model, we use the same EOQ formulas, but
when calculating the holding cost,
we replace Q by Q x (1 – D/P) = QF
Annual holding cost = [ Q x ( 1 – D/P)] x C x (i/2) = Q x F x (Ci/2)
Annual setup cost = D/Q x O
To minimize the total combined cost, we use the same EOQ
formulas, but Q is Q x (1- D/P) for the holding cost.
The value of Q that minimizes the combined cost available
when:
Q(1-D/P)H/2 + DO/Q = QFH/2 + DO/Q
So the optimal value of the order quantity Q is
Q* =
2DO
H(1 - D/P)
The annual cost of holding and ordering (which are equal) is
DxOxH (1  D )
P 
2
DxOxHxF
2
SO the minimum annual combined cost is
2 xDxOxHx(1  D )  2 xDxOxHxF
P
Economic Production Lot Size
Model
•
•
•
•
•
•
•
Production Build-up = (P-D)
Production Duration = Q/P
Maximum Inventory = (P-D)Q/P or (1-D/P)Q
Average Inventory = (1-D/P)Q/2
Time between production starts = Q/D
Number of Production runs per year = D/Q
Total Annual Cost =
AD h(1  D / P)Q
Y(Q) =

 Dc
Q
2
Setups
Holding
Purchase
Economic Production Lot Size
2DO
Q* =
H(1 - D/P)
Zap Electronics
What-If Analysis for Microphones
Demand
Cost per unit
Percent to hold
Ordering cost
Production rate
Lot size
Number of orders
Unit holding cost
Annual holding cost
Annual ordering cost
Combined cost
Annual purchase cost
Total cost
Economi
c
Producti
Model
on
D
12,000
C
$6.75
i
20%
O
28
P
48,000
Q* =sqrt((2DO)/((Ci)*(1-D/P)))
815
N=D/Q
15
H=C*i
$1.35
AHC=(QH/2)*(1-D/P)
$412
NO
$412
QH/2*(1-D/P)+NO
$825
DC
$81,000
$81,825
12000
6.75
0.2
28
48000
=sqrt((2*C4*C7)/((C5*C6)*
=C4/C9
=C6*C5
=(C9*C11/2)*(1-C4/C8)
=C10*C7
=C12+C13
=C5*C4
=C15+C14
CASE1: Brent order 26 times a year, so each additional dollar cost
of ordering should increase annual cost by $26.
CASE 2: If the ordering cost goes up by $1, the combined cost
goes by 17 x $1= $17.
Combined
annual cost
Ordering cost
$1,040
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
831.54
857.54
883.54
909.54
935.54
961.54
987.54
1013.54
1039.54
1065.54
1091.54
1117.54
1143.54
1169.54
1195.54
1221.54
Combined
annual cost
Ordering cost
26.00
$952
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
816.40
833.41
850.42
867.43
884.44
901.45
918.45
935.46
952.47
969.48
986.49
1003.50
1020.50
1037.51
1054.52
1071.53
17.01
CASE 1: What-if the ordering cost goes up 10%? The ordering cost is
$28, so a 10% increase leads to an increase of $2.80. = 26x2.80=72.80
CC=$1039 + $72.80=$1112.80 means increase of 7%.
A 10% increase in ordering cost leads to 7% increase in combined cost.
What about CASE2 ?
% increase in ordering Combined
cost
annual cost
$1,039
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% increase in
ordering cost
Combined
annual cost
$952
1111.98 72.80 7.01%
1184.78
1257.58
1330.38
1403.18
1475.98
1548.78
1621.58
1694.38
1767.18
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
998.96 44.42 4.66%
1043.38
1085.98
1126.98
1166.53
1204.79
1241.87
1277.87
1312.89
1347.00
CASE 1 : What if the interest rate charged as holding cost i changes ?
Only the holding cost changes, and the formula to use is CC= QCi/2
+DO/Q= 1557.6 x i + 728
If the percentages goes to 30%-50% increase, then
CC= 1557.6 x .3 + 728= 467.3 +728= 1195
This is $155 higher than the base-case cost of $1039. To summarize, 50%
increase in the percentage results in a 155/1039=14.9% increase in CC.
What about CASE 2 ?
% Increase in
Interest rate to hold
Combined
annual cost
Ordering cost % Increase in
Interest rate to hold
$1,039
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
$952
883.59 155.59
1039.18 155.59
1194.76 155.59
1350.35
1505.94
1661.53
1817.11
1972.70
2128.29
2283.88
14.97%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
714.35 238.12
952.47
1190.59
1428.71
1666.82
1904.94
2143.06
2381.18
2619.29
2857.41
25.00%
CASE 2 :The minimum cost obtained by using the EOQ is $952.50,
so increasing the order quantity by 10% leads to a total cost
increase of only $4.30, which is only 0.45% of the base cost.
Changing the order quantity by a small amount has very little effect
on the combined cost. And this allow more flexibility in using the
EOQ as a guide to decision making.
What about CASE1?
% Increase in quantity Combined
each order
annual cost
% Increase in quantity Combined
each order
annual
$952 cost
$1,039
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1070.29
1101.41
1132.53
1163.65
1194.76
1225.88
1257.00
1288.12
1319.23
1350.35
31.12
62.23
93.35
124.47
155.59
186.71
217.82
248.94
280.06
311.18
2.99%
5.99%
8.98%
11.98%
14.97%
17.97%
20.96%
23.96%
26.95%
29.94%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
956.80
968.34
985.44
1006.90
1031.84
1059.62
1089.74
1121.80
1155.50
1190.59
4.33
15.87
32.97
54.43
79.37
107.15
137.27
169.33
203.03
238.12
0.45%
1.67%
3.46%
5.71%
8.33%
11.25%
14.41%
17.78%
21.32%
25.00%
What- IF Scenarios
3) The formula are simpler if we use factors instead of percent changes. What if the
unit cost C or the interest rate is I changes by a factor of F, F=1.1 corresponding to
10% increase?
The annual ordering cost does not changes, but the annual holding cost is
multiplied by the factor F, so the formula for the combined cost is
CC=AH x F + AO= 311.50 x F +728
4) What if the ordering cost O changes by a factor of K? The annual holding cost
remains the same but the annual ordering cost changes by the factor K. The formula
to use is
CC=AH+AO x K= 311.50 + 728 x K
Pots
Pots
12,000 12,000
$6.75
$6.75
20%
20%
28
28
461.54 461.54
26
26
$1.35
$1.35
$312
$312
$728
$728
$1,071 $1,112
$81,000 $81,000
$82,071 $82,112
Demand
Cost per unit
Interest rate to hold
Ordering cost
Quantity each order
Number of orders
Unit holding cost
Annual holding cost
Annual ordering cost
Combined cost
Annual purchase cost
Total cost
F
k
Holding Combined
cost
$1,071
0.5
883.8
0.6
914.9
0.7
946.1
0.8
977.2
0.9
1008.4
1
1039.5
1.1
1070.7
1.2
1101.8
1.3
1133.0
1.4
1164.2
1.5
1195.3
1.6
1226.5
1.7
1257.6
1.1
1.1
Ordering
Combined
Cost
$1,112
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
675.54
748.34
821.14
893.94
966.74
1039.54
1112.34
1185.14
1257.94
1330.74
1403.54
1476.34
1549.14
1.8
1288.8
1.8
1621.94
1.9
2
1319.9
1.9
2
1694.74
1351.1
1767.54
Digram 26 Order per Year
2000
1800
1400
Cost
Ordering
EOQ
1039
1600
1200
1000
Holding
800
600
400
200
0
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Cahnge Factor
1.5
1.6
1.7
1.8
1.9
2
EOQ Model With Price Breaks
Discount Quantities
An Inventory ordering situation in which there are small
price breaks when ordering in quantity. These is called
Quantity Discounts.
Quantity discount occur in numerous situations where
suppliers provide an incentive for large order quantities
by offering a lower purchase cost when items are
ordered in larger lots of quantities.
In this section we show how the EOQ model can be used
when quantity discount are available.
EOQ Model With Price Breaks
Discount Quantities
The parameters of the model are as:
Yearly Demand ( D ) = 10000 units
Unit ordering cost (O ) =$30
Inventory holding percentage (I ) = 20%
Unit cost is given as follows:
If Q < 600, then C= $7.50
If 600 >= Q<=1000 then C=$7.48
If 1000 <= Q then C=7.46
The purchasing cost is include in this model because it is not constant
its varying with the discount related to the amount of quantity.
EOQ Model With Price Breaks
Discount Quantities
To get the total annual cost, we need to add three annual costs:
Annual holding cost :
AH = Q x C x I/2
Annual ordering cost :
AO = D x O/Q
Annual purchasing cost : C x D
If Q < 600, then C= $7.50
Total = 1000 * 7.5 * 0.2/2 + 10,000 * 30/1000 + 7.5 * 10,000 = 76,050
If 600 >= Q<=1000 then C=$7.48
Total = 1000 * 7.48 * 0.2/2 + 10,000 * 30/1000 + 7.48 * 10,000 = 75,848
If 1000.<= Q then C=7.46
Total = 1000 * 7.46 * 0.2/2 + 10,000 * 30/1000 + 7.46 * 10,000 = 75,646
D
I
10,000 O
20.00%
C
30
IF Q < 600
IF 600 <= Q <= 1000
IF 1000 <= Q
Que ntity
7.5
7.48
7.46
C
400
450
500
550
600
650
700
750
800
850
900
950
1000
1050
1100
1150
1200
1250
1300
1350
Annua l
holding
cost
300
337.5
375
412.5
448.8
486.2
523.6
561
598.4
635.8
673.2
710.6
746
783.3
820.6
857.9
895.2
932.5
969.8
1007.1
7.5
7.5
7.5
7.5
7.48
7.48
7.48
7.48
7.48
7.48
7.48
7.48
7.46
7.46
7.46
7.46
7.46
7.46
7.46
7.46
Annua l
orde ring
cost
750
666.7
600.0
545.5
500.0
461.5
428.6
400.0
375.0
352.9
333.3
315.8
300.0
285.7
272.7
260.9
250.0
240.0
230.8
222.2
Annua l
purcha sing
cost
75,000
75,000
75,000
75,000
74,800
74,800
74,800
74,800
74,800
74,800
74,800
74,800
74,600
74,600
74,600
74,600
74,600
74,600
74,600
74,600
Tota l cost
76,050
76,004
75,975
75,958
75,749
75,748
75,752
75,761
75,773
75,789
75,807
75,826
75,646
75,669
75,693
75,719
75,745
75,773
75,801
75,829
76,100
76,000
75,900
75,800
75,700
75,600
75,500
1350
1300
1250
1200
1150
1100
1050
1000
950
900
850
800
750
700
650
600
550
500
450
400
75,400
EOQ with C = 7.5
Q = SQRT( 2*10,000*30/(7.5*.2)) = 632.45
EOQ with C = 7.48
Q = SQRT( 2*10,000*30/(7.48*.2)) = 633.31
Minimum
at C = 7.48
EOQ with C = 7.46
Q = SQRT( 2*10,000*30/(7.46*.2)) = 634.14
When
. purchase depends on quantity, the total global or overall minimum
is either at a point where the slope is zero, as identified by the EOQ
formula, or where is a price break.